摘要
给出了一个含有参数λ的五次多项式基函数,是四次Said-Ball曲线基础函数的扩展;分析了此基函数的性质,基于该组基函数定义了带有形状参数的多项式曲线.曲线不仅具有四次Said-Ball曲线的特性,而且具有形状的可调性和更好的逼近性.参数λ有明确的几何意义:λ越大,曲线越逼近控制多边形;当λ=0时,曲线退化为四次Said-Ball曲线.还讨论了两段曲线C1连续拼接的条件.实例表明,定义的曲线的形状是随着λ取不同的值而发生变化.
Abstract： A class of polynomial basis function of 5th degree with shape control parameter λ is presented. It is extension of basis function of quartic Said-Ball curve. Properties of this new basis are analyzed and the corresponding polynomial curve with a shape paramete λ is defined. This curve not only inherit the outstanding properties of quartic Said-Ball curve, but also is adjustable in shape and fit close to the control polygon. This curve converge to quartic Said-Ball curve when λ= 0. The C^1-continuity condition of two-piece of curves is also discussed. Some examples illustrate the variation curve shapes with different values of λ.
出处
《纺织高校基础科学学报》
CAS
2009年第2期245-249,共5页
Basic Sciences Journal of Textile Universities
基金
北京市属市管高等学校人才强教计划资助项目(07306)
